Bayesian perspective of the unconventional approach for assimilating aliased radar radial velocities

Abstract

The global minimization problem for directly assimilating aliased radial velocities is derived in terms of Bayesian estimation by folding the domain of the original Gaussian non-aliased observation probability density function (pdf) into the Nyquist interval. By truncating the folded tails of the observation pdf, the observation term in the costfunction recovers the aliased observation term formulated previously by an unconventional approach. This establishes the theoretical basis for the unconventional approach and quantifies the involved approximation. The alias-robust radar wind analysis developed based on the unconventional approach is also revisited from the Bayesian perspective.